AI 中文总结
该研究针对带单一装卸服务器的两台相同并行机器的总完工时间最小化问题，证明其NP完全性，分析列表调度和最长处理时间规则的近似比，揭示处理时间粒度与短作业阻塞对近似性能的影响。
AI 中文摘要
我们研究在两台相同并行机器上的总完工时间最小化问题，这两台机器共享一个用于装卸的单一服务器。每个作业必须先被加载，然后在其分配的机器上无中断地处理，处理完成后立即卸载，所有装卸操作具有共同的正整数持续时间。我们证明，对于每个固定的服务器操作持续时间，该决策问题是NP完全的；当该持续时间作为输入的一部分时，它是强NP完全的。随后，我们在非单位设置下分析普通列表调度算法和最长处理时间规则：列表调度算法的紧上界比为2；对于最长处理时间规则，我们得到当所有处理时间至少为服务器操作持续时间时的精确最坏情况比，并为无限制实例推导了新的依赖参数的上下界。结果表明，处理时间粒度和短作业产生的阻塞共同影响了通用服务器问题的近似行为。
英文摘要
We study makespan minimisation on two identical parallel machines that share a single server for both loading and unloading. Each job must be loaded, processed without interruption on its assigned machine, and unloaded immediately after processing, with a common positive integer duration for all loading and unloading operations. We prove that the decision problem is NP-complete for every fixed server-operation duration and strongly NP-complete when this duration is part of the input. We then analyse ordinary list scheduling and the longest-processing-time rule in the non-unit setting. List scheduling has a tight supremum ratio of two. For the longest-processing-time rule, we obtain the exact worst-case ratio when all processing times are at least the server-operation duration, and derive new parameter-dependent lower and upper bounds for unrestricted instances. The results show that both processing-time granularity and blocking generated by short jobs shape the approximation behaviour of the common-server problem.
Comments29 pages, 1 appendix
